# Stratified Non-Probability Sampling

#### rassta: Raster-based Spatial Stratification Algorithms

Get the data required for this vignette

    # Compressed folder with files from rassta’s installation folder
    wasoil <- system.file("exdat/wasoil.zip", package = "rassta")
    # Directory for temporary files
    o <- tempdir()
    # Copy compressed folder to directory for temporary files
    file.copy(from = wasoil, to = o)
    #> [1] TRUE

    # Extract files to subfolder
    d <- paste(o, "/rassta", sep = "")
    unzip(paste(o, "/wasoil.zip", sep = ""), exdir = d)

The use of stratification units for sampling allows adequate representations of the feature space, improved modeling performance, and cost-efficient field work. Accordingly, rassta allows the stratified selection of observations from an existing sample and the selection of XY locations to create a new sample. The stratified sampling with rassta can include the landscape similarity layers. Accounting for the landscape similarity will ensure that the observation/location selected for a given stratification unit is the one which best reflects the landscape configuration represented by the unit. The use of landscape similarity layers in the sampling process results in a stratified, non-probability sample.

## Selection of representative observations

The selection of observations from an existing sample with rassta results in one observation per stratification unit in a set. This observation is termed the representative response observation. The representative response observation is assumed to best reflect the control that the landscape configuration represented by a stratification unit exerts on response phenomena. Currently, rassta allows to select a representative response observation for each stratification unit in a set based on the following methods:

- mls: selects the observation at the location with the maximum landscape similarity value.
- mrv: selects the observation whose response value is the median of all the values.
- random: selects an observation at random.

The first two methods represent a stratified non-probability sampling, while the third method represents a stratified random sampling. Moreover, the first method is biased towards maximizing the representativeness of landscape configurations because it uses landscape similarity layers. The codes below demonstrate the selection of representative response observations with observation(). The observations will be selected from a sample of n = 195 based on the mls method.

- Creation of multi-layer SpatRaster with landscape similarity to stratification units.

    # Load rassta and terra packages
    library(rassta)
    library(terra)
    # Single-layer SpatRaster of stratification units
    su <- rast(paste(d, "/su.tif", sep = ""))
    # Multi-layer SpatRaster with spatial signatures of classification units
    clim.sig <- rast(list.files(d, pattern = "climate_", full.names = TRUE)) # For climatic units
    mat.sig <- rast(list.files(d, pattern = "material_", full.names = TRUE)) # For material units
    terr.sig <- rast(list.files(d, pattern = "terrain_", full.names = TRUE)) # For terrain units
    # Landscape similarity to stratification units
    su.ls <- similarity(su.rast = su, sig.rast = c(clim.sig, mat.sig, terr.sig),
                        su.code = list(climate = c(1, 1),
                                       material = c(2, 2),
                                       terrain = c(3, 3)
                                       )
                      )

- Selection of the representative response observation for each stratification unit. The response variable in this example is soil organic carbon (SOC).

    # SpatVector with SOC observations for stratification units
    socobs <- vect(paste(d, "/soc.shp", sep = ""))
    # Representative SOC observation for each stratification unit
    su.obs <- observation(su.rast = su, obs = socobs, col.id = 1, col.resp = 2,
                          method = "mls", ls.rast = su.ls$landsim
                          )
    # Information about sample and representative SOC observations
    socobs
    #>  class       : SpatVector
    #>  geometry    : points
    #>  dimensions  : 195, 2  (geometries, attributes)
    #>  extent      : 284252, 292532, 153471, 161811  (xmin, xmax, ymin, ymax)
    #>  source      : soc.shp
    #>  coord. ref. : NAD83 / Washington South (EPSG:32149)
    #>  names       :    ID   soc
    #>  type        : <int> <num>
    #>  values      :     1 6.603
    #>                    2 5.701
    #>                    3 5.594

    su.obs$su_repobs.sp
    #>  class       : SpatVector
    #>  geometry    : points
    #>  dimensions  : 56, 4  (geometries, attributes)
    #>  extent      : 284252, 292532, 153651, 161811  (xmin, xmax, ymin, ymax)
    #>  coord. ref. : NAD83 / Washington South (EPSG:32149)
    #>  names       :    ID   soc    SU land_sim
    #>  type        : <int> <num> <int>    <num>
    #>  values      :     1 6.603   111    80.67
    #>                    6 5.443   112       85
    #>                   10 4.609   114    77.33

- The spatial and statistical distribution of the sample and representative response observations can be plotted as demonstrated in the code below.

    # Set graphics arrangement
    par(mfrow = c(1,2))
    # Plot stratification units and response observations
    plot(su, type = "classes", col = hcl.colors(56, "spectral"), legend = FALSE,
         mar = c(3, 2, 3, 1.5), main = paste("Soil Organic Carbon Observations"),
         fun = function() c(points(socobs, pch = 21, bg = rgb(0,1,0,1)),
                            points(su.obs$su_repobs.sp, pch = 21, bg = rgb(0,0,1,1))
                          )
        )
    # Set new graphics arrangement
    par(mar = c(2, 1.5, 1.5, 1.5))
    # Plot histogram of soil organic carbon values from all observations
    hist(socobs$soc, 4, col = rgb(0,1,0,0.8), main = "Soil Organic Carbon (%)", xlab = "")
    # Plot histogram of soil organic carbon values from representative observations
    hist(su.obs$su_repobs.sp$soc, 4, add = T, col = rgb(0,0,1,0.9))
    # Add legend
    legend("topright", legend = c("Sample", "Representative Observations"),
           col = c(rgb(0,1,0,0.8), rgb(0,0,1,0.9)), pch = 20, bty = "n", pt.cex = 2,
           cex = 0.6, text.col = "black", horiz = F, inset = c(0, 0.05)
          )

## Selection of representative sampling locations

For those cases when a sample with observations of a response phenomenon is not available, rassta allows to define XY locations that can be used to establish field sampling campaigns. The selection of representative sampling locations is performed for each stratification unit in a set, and it utilizes the landscape similarity layers to define the XY locations. Currently, rassta allows to select representative sampling locations based on two approaches:

- buffer: selects the XY location(s) within spatially contiguous areas with landscape similarity values above a user-defined threshold.

- absolute: selects the XY location(s) with the n highest landscape similarity values.

The code below demonstrates the selection of representative sampling locations with the function locations(), based on the buffer method.

    # Representative sampling location and its buffer area for each stratification unit
    su.samp <- locations(ls.rast = su.ls$landsim, su.rast = su, method = "buffer")
    # Information about representative sampling locations and corresponding buffer areas
    su.samp$locations
    #>  class       : SpatVector
    #>  geometry    : points
    #>  dimensions  : 90, 2  (geometries, attributes)
    #>  extent      : 284072, 292532, 153351, 161841  (xmin, xmax, ymin, ymax)
    #>  coord. ref. : NAD83 / Washington South (EPSG:32149)
    #>  names       :    SU land_sim
    #>  type        : <num>    <num>
    #>  values      :     1    66.33
    #>                    1    66.33
    #>                    1    69.67

    su.samp$buffers
    #>  class       : SpatVector
    #>  geometry    : polygons
    #>  dimensions  : 56, 2  (geometries, attributes)
    #>  extent      : 284027, 292547, 153336, 161856  (xmin, xmax, ymin, ymax)
    #>  coord. ref. : NAD83 / Washington South (EPSG:32149)
    #>  names       :    SU      area
    #>  type        : <num>     <num>
    #>  values      :   111 9.182e+04
    #>                  112 1.026e+05
    #>                  113 1.206e+05

The spatial distribution of representative sampling locations and the statistical distribution of landscape similarity can be plotted as demonstrated in the code below.

    # Set graphics arrangement
    par(mfrow = c(1,2))
    # Plot stratification units, representative sampling locations and buffer areas
    plot(su, type = "classes", col = hcl.colors(56, "spectral"), legend = FALSE,
         mar = c(3, 2, 3, 1.5), main = "Representative Sampling Locations",
         fun = function() c(polys(su.samp$buffers, col = rgb(0,1,0,0.5)),
                            points(su.samp$locations, pch = 21, col = "black",
                                   bg = rgb(0,1,0,1)
                                  )
                          )
        )
    # Set new graphics arrangement
    par(mar = c(2, 1.5, 1.5, 1.5))
    # Plot histogram of landscape similarity values at sampling locations
    hist(su.samp$locations$land_sim, 4, main = "Landscape Similarity")

Clean files from temporary directory

    unlink(c(paste(o, "/wasoil.zip", sep = ""), d), recursive = TRUE)

## References

- B.A. Fuentes, M.J. Dorantes, and J.R. Tipton. rassta: Raster-based Spatial Stratification Algorithms. EarthArXiv, 2021. https://doi.org/10.31223/X50S57